PreprintarXiv licencearXiv
Arithmeticity of critical L-values for Hilbert-Siegel modular forms in the left half plane and s = 1
Abstract
For a cuspidal automorphic representation πf generated by a Hilbert-Siegel modular form f and a Hecke character μ with parallel signature, we show the arithmeticity of critical L-values of the standard L-function LS(s,πf, μ) twisted by μ in the left half plane. As a consequence, we show the arithmeticity at s=1 under the assumption that there exists a nonarchimedean place v such that πv is unramified and μv is ramified.
Related
- Reducible fibers of polynomials over integers: the Hilbert-Siegel problem over ℚ and its applications
- Arithmetic Siegel--Weil formula on the product of modular curves
- The number of Ekedahl-Oort strata intersecting the supersingular locus in the Siegel modular variety
- Biggest bounded type Siegel disks of monic polynomials include those that stick to all critical points
- The Shimura Lift and Hilbert Modular Forms
BibTeX
@misc{horinaga2026arithmeticity,
title = {{Arithmeticity of critical $L$-values for Hilbert-Siegel modular forms in the left half plane and $s = 1$}},
author = {Shuji Horinaga and Hirotaka Kakuhama},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23037},
eprint = {2610.23037},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23037},
}
RIS
TY - UNPB
TI - Arithmeticity of critical L-values for Hilbert-Siegel modular forms in the left half plane and s = 1
AU - Shuji Horinaga
AU - Hirotaka Kakuhama
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23037
UR - https://arxiv.org/abs/2610.23037
AB - For a cuspidal automorphic representation π_f generated by a Hilbert-Siegel modular form f and a Hecke character μ with parallel signature, we show the arithmeticity of critical L-values of the standard L-function L^S(s,π_f, μ) twisted by μ in the left half plane. As a consequence, we show the arithmeticity at s=1 under the assumption that there exists a nonarchimedean place v such that π_v is unramified and μ_v is ramified.
ER -